Life-cycle cost-based design procedure to determine the optimal environmental design load and target reliability in offshore installations

Structural Safety 59 (2016) 96–107

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Life-cycle cost-based design procedure to determine the optimal environmental design load and target reliability in offshore installations Seong-yeob Lee a, Choonghee Jo a, Pål Bergan a, Bjørnar Pettersen b, Daejun Chang a,⇑ a Graduate School of Ocean Systems Engineering, Department of Mechanical Engineering, Korea Advanced Institute of Science & Technology (KAIST), 291 Daehak-ro, Yuseong-gu, Daejeon 305-701, Republic of Korea b Department of Marine Technology, Norwegian University of Science and Technology (NTNU), NO-7491 Trondheim, Norway

a r t i c l e

i n f o

Article history: Received 24 September 2014 Received in revised form 26 August 2015 Accepted 26 December 2015

Keywords: Optimal environmental design load Target reliability Life-cycle cost (LCC) Marine structure

a b s t r a c t This study proposed a design procedure for determining optimal design load and reliability for offshore installations. The life-cycle cost (LCC) was estimated for a range of characteristic environmental loads. An iterative design optimization procedure was employed to find the target reliability at which the LCC was minimized. The structural system was designed for a given set of environmental loads caused by waves, currents, and winds. Extreme environmental conditions were estimated by a probabilistic model. The relationship between the characteristic load and the structural reliability was considered on the basis of the selected probabilistic model to study the variation of the LCC for the given set of environmental loads. The set of LCCs, which were the sum of the capital expenditure (CAPEX), operating expenditure (OPEX), and risk expenditure (RISKEX), were estimated to determine the optimal reliability. A case study was conducted for a pile-guide system (PGS) as a novel offshore installation. The PGS was designed to keep the position of large-scale floating installations. The system consists of guide piles supporting the floating installation, a subsea truss structure cross-linking the piles, and a seabed base platform fixed to the seabed. Two target locations near Busan city were considered to study the change of optimal reliability with respect to the same structural system. Finally, the optimal reliabilities at the two target locations were determined with the minimum LCC. The optimal reliability could vary depending on the types of structures, the economic roles of the system, and the environmental conditions at various locations. Thus, in contrast to the prescriptive strategy, the proposed procedure for determining the optimal design load and reliability would be meaningful and applicable to design of offshore structures. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction Basically, an offshore structure construction project is performed as the following procedure: investment feasibility studies, construction site survey including diving inspections of installation locations, conceptual design, detailed design and structure element strength calculations, design-approval by the regulating authorities, procurement, fabrication, and installation. Safety criteria of structures including design load and target reliability are generally determined at the conceptual design stage even though structural data are insufficient. Thus, determination of design load and target reliability has been conducted in accordance with recommendations published by the classification society [35]. Many studies computing structural reliability for offshore structures have been carried out. Mousavi, Gardoni, and Maadooliat ⇑ Corresponding author. Tel.: +82 42 350 1514; fax: +82 42 350 1510. E-mail address: [email protected] (D. Chang). http://dx.doi.org/10.1016/j.strusafe.2015.12.002 0167-4730/Ó 2016 Elsevier Ltd. All rights reserved.

(2013) proposed the Progressive Reliability Method (PRM) to quantify the reliability of complex offshore structures. A mooring system was considered for the case study, and the results of PRM were compared with those of Monte Carlo simulation that was a basic method to compute the reliability [29]. Mousavi and Gardoni (2014) also defined the concept of integrity index in order to measure and to maximize the balance of reliability of system components [30]. A simplified method for the reliability and the integrity-based optimal design was presented and illustrated considering offshore mooring systems. Finally, the computed reliability was compared with target reliability (10
4) recommended by the classification society to check whether it was acceptable or not [31]. In designing offshore structures, codes and standards from the classification society have been employed in prescriptive ways although optimal reliability criteria can vary depending on the types of structures, economic characteristics, and installation locations. Alternative methods for determining the optimal design load

S.-y. Lee et al. / Structural Safety 59 (2016) 96–107

and reliability for offshore structures have not been well established thus far. That is why the criteria for a characteristic load and target reliability have been selected on the basis of satisfactory experiences only and not of any rigorous considerations. The International Organization for Standardization (ISO), Det Norske Veritas (DNV), American Petroleum Institute (API), and Korea Register (KR) commonly recommend a 100-year return period for extreme environmental characteristic loads caused by waves, currents, and wind [2,11–13,16,21]. The criteria for offshore structural designs have been specified in terms of factors related to loads caused by 100-year environmental conditions. Target reliability levels are also recommended in existing codes. API RP 2A LRFD designates the average annual failure probability (Pf) as 4  10
4 per year. The Canadian Standards Association defines two safety classes and a serviceability class for verification of the safety of a structure or any of its structural elements. 10
5 is recommended for great risk to life and 10
3 is for small risk to life [4]. DNV suggested that the minimum target reliability values should be calibrated against well-established cases that are known to exhibit adequate safety. 10
4 for less serious consequences and 10
5 for serious consequences are recommended by DNV with respect to significant waring prior to the occurrence of failure in a non-redundant structure [10]. The concepts of life-cycle cost (LCC) have been employed to determine the target reliability in onshore structures, including buildings and bridges. Koskisto and Ellingwood (1997) presented the systematic procedure to find the optimal design of precast concrete from the life-cycle cost point of view [32]. Ang and De Leon (1997) proposed a systematic approach involving risk-based costeffective criteria for reinforced concrete buildings in Mexico City in relation to various seismic loads [1]. The reliability index and the expected LCC were analyzed by Kim et al. (2013) to determine the optimal target reliability in a case study on a bridge [19]. Most previous studies have taken into account the initial construction costs, operation and maintenance costs, and demolition and disposal costs. Only the operation and maintenance costs are considered to be probabilistic, even though initial investments could be related to structural reliability. Ang and De Leon (1997), Li and Cheng (2001), and Kim et al. (2013) determined initial costs as a function of structural target reliability but argued that it was difficult to determine the relationship between the initial construction cost and target reliability [1,19,27]. In the offshore field, equations to estimate the LCC of onshore structures cannot be used for newly developed offshore installations. Bhattacharya, Basu, and Ma (2001) attempted to illustrate the methodology for determining the target reliability of the US Navy’s Mobile Offshore Base (MOB) that is a unique offshore structure [3]. This study focused on numerical target reliability on the basis of various structural standards. Val and Stewart (2003) performed life-cycle cost analysis to select optimal strategies improving durability of RC structures in marine environments. Their study focused on corrosion of carbon steel reinforcement induced by chloride to consider the spalling failure [9]. Moan (2011) concentrated on structural fatigue failure and studied the adequate design, inspection, monitoring, and repair procedures based on life-cycle safety management of offshore structures [37]. Mullard and Stewart (2012) performed life-cycle cost analysis considering repair and user delay costs to find the appropriate timing and extent of maintenance actions with respect to reinforced concrete structures [17]. Yang et al. (2013) established the deterioration model for a long life-span of the reinforced concrete structures, and studied optimal maintenance strategies based on cost estimation of three maintenance levels [28]. Jung et al. (2013) updated the probabilistic LCC model based on Bayesian approach for reinforced concrete structures to find an optimum repair and

97

reinforcement timing [15]. Laura and Vicente (2014) made a formula to calculate life-cycle cost of floating offshore wind farms. Three types of platforms were considered and compared each other [5]. Many studies focused on finding an optimal maintenance timing after the conceptual design stage. Determination of criteria at the early design stage is a pretty important task from an economic point of view, and target reliability can vary depending on types of structures, locations, and economic roles of marine structures. However, target reliability of offshore structures have been generally determined by using codes of the classification society. Few studies have considered criteria of reliability from whole life-cycle cost point of view [25]. Thus, the study on determination of optimal reliability based on life-cycle cost analysis is required for newly developed marine structures at the conceptual design stage even though information and experiences of structures are insufficient. This study proposes a practical method for determining the optimal reliability criteria of offshore installations at the conceptual design stage. Return periods of characteristic loads and design loads are taken into consideration to study the relationship between target reliability and life-cycle costs. The suggested procedure for obtaining the optimal reliability is delineated in Section 2. The Pile Guide System (PGS) that is a novel support structure for offshore mega-floaters is considered for a case study in Section 3. Busan New Port and Busan North Port in the Republic of Korea are selected as the target locations. Finally, the optimal design load and reliability of the PGS structure at the two target locations are determined with the minimum LCC and compared with present reliability criteria recommended by the classification society in Section 4. 2. Design optimization procedure based on life-cycle cost analysis When the strength of the offshore installations is increased to prevent structural damage and economic losses, the initial investment in the structures also increases. Therefore, a practical, realistic method that is helpful for determining an optimal design load and target reliability in terms of the ultimate strength will be required for offshore installations from the whole life-cycle cost point of view. The suggested design procedure for generating risk-based designs is shown in Fig. 1:

Fig. 1. Design procedure for LCC analysis.

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2.1. Step 1: Probabilistic modeling of extreme environmental conditions Data on extreme environmental conditions, which include significant wave heights, current velocities, and wind velocities at an actual location, are required to estimate the characteristic loads acting on an offshore structure. The extreme environmental conditions corresponding to the return period can be estimated with extreme distribution functions, such as the Gumbel distribution (Type I), Frechet distribution (Type II), and Weibull distribution (Type III). The appropriate probabilistic model changes depending on the target location. Many studies have been conducted to compute gust wind velocity and significant wave height with probabilistic models. Lee et al. (2010) estimated extreme wind speeds using a national wind map with Gumbel & Weibull distributions in relation to the structural stability of a wind power plant station hub [23]. Jung (2012) performed a stochastic estimation of wind speed as affected by a typhoon for three different sites (Ulsan, Yeonggwang, and Geoge in Korea) where long span bridges were located [18]. In order to study waves directly, Kwon et al. (1991) employed a statistical method for estimation of extreme sea levels with the Weibull distribution function [22]. Lee et al. (1992) developed computational methods based on the Weibull distribution for estimation of extreme sea levels [26]. Ryu and Kim (2004) studied the statistical properties of extreme waves in Hong-do, an island in Korea, during typhoons [34]. A study on the projection of future wave climate changes was conducted by Park et al. (2013) [33]. Other extreme distribution function, for instance, Exponentiated Gumbel (EG) distribution was proposed to estimate return levels of wave heights exactly for a specific location [20]. Accumulated environmental data are required to select an appropriate probabilistic model that satisfactorily represents actual measurement data at a target location. Wind speed varies with time and with the height above the ground or the sea surface. A commonly used reference height is 10 m, and generally employed averaging times are 1 min or 10 min for short-term conditions. If accumulated data are not available with respect to waves at the target location, a simplified equation can be used for the relationship with the mean wind velocity. 2.2. Step 2: Calculation of characteristic environmental loads for a set of return periods At this stage, a set of return periods are studied, for example, 30, 50, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 3000, 5000, and 10,000 years. The return periods from 100 to 1000 years should be dense because this is the important interval for the optimal characteristic load. Extreme environmental conditions, which include significant wave heights and wind velocities for each return period, can be estimated using the selected probabilistic model. The joint occurrence of waves, currents, and wind should be considered to take into account the most severe characteristic load for each return period. The characteristic loads acting on the offshore structure can be calculated by commercial codes. ANSYSAQWA, SESAM-HydroD, or SESAM-GeniE can be employed to calculate characteristic loads with the estimated environmental conditions. 2.3. Step 3: Structural design for each design load Load and resistance factor design (LRFD) is employed in designing offshore structure based on characteristic loads. LRFD is a design method in which uncertainties in characteristic loads are

represented with a load factor, and uncertainties in the resistance of the materials are represented with a material factor [11]. The design load is obtained through multiplying the characteristic load and the load factor. To consider the relationship between the initial investment and the design load, the cross-sections of the main components of the target structure are considered for each design load. The initial dimensions of the main components are determined on the basis of simplified models and basic equations. The initial dimensions will be used as the starting point of the iteration for the crosssectional optimization. The objective of this cross-sectional optimization is to minimize the total weight of the target structure. The radii and thicknesses of the main components can be determined for the design variables. The geometry and topology of the target structure are not considered in the optimization. Only their cross-sectional area is taken into account to study the change in the structural design for each design load. The optimization results are obtained from an optimization program with a 2D model to save iteration time. The 15 final models for each design load should be confirmed using a 3D solid model for correct results. Finally, all of the dimensions of the main components can be determined for 15 design loads. The set of structures will be used to consider the relationship between the initial investment and structural reliability.

2.4. Step 4: Relationship between the characteristic load and structural reliability The calculated characteristic loads are well fitted by the selected probabilistic model of extreme environmental conditions. The design load is obtained through multiplication of the characteristic load and the load factor because LRFD method is employed. When an engineer selects the characteristic load for a structural design, the structure will be designed with the design load due to the load factor. The return period of the design load should be estimated to consider the relationship with the structural reliability. Reliability is closely related to the annual probability of failure of the structure. The probability of failure per annum can be calculated on the basis of the return periods of the characteristic loads, which was considered in the selected extreme distribution function in the first step. Eq. (1) and Fig. 2 show the proposed procedure for calculating the return period of the design load. T1 is a return period of a characteristic load, and T2 is a return period of a design load. The solid line indicates extreme environmental loads (the characteristic load) for each return period, and the dotted line expresses the design load. The annual probability of failure can be computed as the inverse of the return period of the design load. Note that the relationship between the return period of the characteristic load and the annual probability of failure depends on load factors and probabilistic models.

Characteristic load ¼ LoadðT1Þ T2 ¼ f


1

ðLoad factor  LoadðT1ÞÞ

ð1Þ

Classification of damage states is required because the extent of damage to the structure depends on the intensity of the external load. Four damage states (insignificant damage, minor damage, significant damage, and severe damage) are considered to compute more accurate damage costs [14]. The load factors for each damage state can be obtained on the basis of the results of finite element analysis. Four probabilistic failures for each damage state can be calculated as the inverse value of the return period corresponding to multiplication of the load factors and the characteristic loads by Eq. (1).

S.-y. Lee et al. / Structural Safety 59 (2016) 96–107

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Fig. 2. Procedure to calculate return period of design load.

2.5. Step 5: LCC estimation for each structural design The LCC is analyzed to determine the optimal environmental design load and reliability of an offshore installation. Initial construction costs, operation, maintenance, and repair costs have been generally estimated for LCC analysis in terms of structural design. Thus, this study takes Capital expenditure (CAPEX), Operating expenditure (OPEX), and Risk expenditure (RISKEX) into consideration to compute the LCC as shown by Eq. (2) [6]. RISKEX is the failure risk expenditure due to an extreme environmental load in this research. Some assumptions are necessary in order to analyze the LCC because determination of design load and reliability is generally performed at the conceptual design stage.

LCC ¼ CAPEX þ OPEX þ RISKEX

ð2Þ

The CAPEX is the initial investment to make a structure. This research first considers the return periods of characteristic loads to study the relationship between the CAPEX and the return periods of the design loads, and the relationship between the return periods of the design loads and structural reliability is taken into consideration. Eq. (3) expresses the CAPEX, which consists of manufacturing costs (Cm), transport costs (Ct), and installation costs (Ci). The CAPEX can be estimated on the basis of manufacturing costs that is calculated from the dimensions of the main components of the structure. a is coefficient of manufacturing costs for CAPEX.

CAPEX ¼ C m þ C t þ C i ¼ C m  a

ð3Þ

The OPEX is the regular maintenance costs for marine structures, which include the replacement of expendables and corrosion checks. Thus, the difference in the OPEX for each design load is insignificant compared with other expenditures. The OPEX can be estimated based on the CAPEX according to Eq. (4). The present worth factor (Pw) should be considered because the OPEX and the RISKEX represent the expected cost or loss during the lifespan of the target structure [1,19]. LS is lifespan of the marine structure, and b is coefficient of the CAPEX for the OPEX.

OPEX ¼ b  CAPEX  LS  Pw

ð4Þ

When the structural system is designed in relation to the specific time period of the design load, the probability of structural failure can be estimated on the basis of the selected probabilistic

model. The RISKEX, which includes replacement costs and the economic loss from the damaged structure during its design life, can be estimated from the annual probability of failure. The RISKEX is calculated through the multiplication of damage costs (Cd), the annual probability of failure (Pf), the lifespan of the structure (LS), and the present worth factor (Pw) according to Eq. (5).

RISKEX ¼

X

C d Pf  LS  Pw

ð5Þ

The damage costs per annum can be estimated by Eq. (6). The annual loss caused by extreme environmental loads is determined through the multiplication of damage costs (Cd) and the probability of failure per annum (Pf) for the four damage states. Cdis is the damage costs for insignificant consequences, Cdm is damage costs for minor consequences, Cds is the damage costs for significant consequences, Cdsv is the damage costs for severe consequences, Pfis is annual probability of failure for insignificant consequences, Pfm is annual probability of failure for minor consequences, Pfs is annual probability of failure for significant consequences, and Pfsv is annual probability of failure for severe consequences.

X

C d Pf ¼ C dis P fis þ C dm Pfm þ C ds Pfs þ C dsv Pfsv

ð6Þ

Eq. (7) shows the components of the damage costs for each damage state [1]. They consist of the costs of repair or replacement, rental fee for heavy lift vessels (HLVs), and the economic loss. The replacement costs are to consider failed components induced by extreme loads, and the costs of HLVs are the biggest part of installation costs [38]. Economic loss is estimated to consider business interruption during repair and replacement times.

C dis ¼ C ris þ C cis þ C eis C dm ¼ C rm þ C cm þ C em C ds ¼ C rs þ C cs þ C es

ð7Þ

C dsv ¼ C rsv þ C csv þ C esv ; where Cris is the repair and replacement costs for insignificant consequences, Crm is the repair and replacement costs for minor consequences, Crs is the repair and replacement costs for significant consequences, Crsv is the repair and replacement costs for severe consequences, Ccis the rental fee for offshore crane vessels for insignificant consequences, Ccm is the rental fee for offshore crane vessels for minor consequences, Ccs is the rental fee for offshore crane vessels for significant consequences, Ccsv is the rental fee for offshore crane vessels for severe consequences, Ceis is the economic

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loss for insignificant consequences, Cem is the economic loss for minor consequences, Ces is the economic loss for significant consequences, and Cesv is the economic loss for severe consequences. In order to calculate the present worth factor (Pw), the average interest rate and the average inflation rate are investigated, and the discount rate (d) is determined as the difference between the two. Eq. (8) explains the series present worth factor, which translates a series of uniform values of the annual RISKEX into the present worth [41]. LS

Pw ¼

ð1 þ dÞ
1 LS

dð1 þ dÞ

=LS;

New Port be an international logistics center port for Northeast Asia. In accordance with the relevant technical report [24], many offshore structures will be installed near Busan New Port. Location A has pretty good environmental conditions to consider the LNGBT. The other is Location B near Busan North Port. Environmental conditions at the port is more severe than those of Location A. Location B is selected to study change of optimal reliability with respect to the same structural system. Optimal reliability can vary depending on target locations even though same structural system is designed.

ð8Þ

2.6. Step 6: Finding the optimal reliability with the minimum LCC Finally, the set of LCCs for each structural design will be obtained, and the optimal characteristic load can be determined with the minimum LCC. The optimal characteristic load can differ depending on the load factor determined by the designer. However, the optimal reliability cannot be changed when the same structure and the location are taken into account. The optimal reliability will be obtained from the relationship with the return period of the design load. This result is compared with the target reliability recommended by the classification society. 3. Case study: Pile Guide System (PGS) 3.1. Background of the case study As coastal areas have continued to provide sites for energy development and utilization, mega-scale floaters have played a critical role in various energy sectors, and their role will undoubtedly continue to increase in the future. Thus, many technologies have been developed to support offshore installations. In the case study examined in the present work, the PGS, a positionmaintaining solution for mega-scale floaters, is considered. Heavy fuel oil (HFO) has been the main fuel resource used for ship propulsion. Nowadays, liquefied natural gas (LNG) is being considered more and more as a new fuel for ship propulsion because of the significant environmental problems associated with HFO. In order to use LNG as fuel for ships, infrastructure will be needed for a newly developed refueling system. The LNGBunkering Terminal (LNG-BT) that is the infrastructure for the refueling system is employed as the target system of the PGS [42]. The PGS (shown in Fig. 3) is a new type of supporting structure for mega floaters based on the combined principle of jacket structures and floating type installations. The floater for LNG-BT is designed to be 276 m long, 56 m wide, and 28 m depth. The draft is to be maintained at 11 m. Multiple piles are mounted on a floater and connected to truss structures and the seabed base platform, which are fixed to the seabed with fixing piles. The components connecting the floater and the guide pile are specially designed to allow the massive floater to exhibit vertical motions only in accordance with draft and the water level. The seabed truss structure will prevent the guide piles from moving horizontally in response to environmental loads applied to the floater. The truss structure consists of pile housings for inserting the guide-piles and cross-linked pipes. It is easy for the inserted piles to make a replacement if they fail. The PGS don’t need to withstand deadweight of the floater because it can move up and down freely along the guide piles. Only horizontal forces, leading to the pure bending moment in the guide piles, are taken into consideration. For the case study, two ports near Busan city in Republic of Korea are selected as target locations. One is Location A near Busan New Port. The Busan Port Authority (BPA) has a plan to make Busan

3.2. Step 1: Probabilistic modeling of extreme environmental conditions Among the available extreme distribution functions, the Gumbel distribution is employed in step 1 because this distribution function coincides with actual measurement values obtained in Korea and can provide conservative values compared with other distribution functions [23]. This section describes the extreme weather conditions at the target sites, including the instantaneous wind velocity, current velocity, and the significant wave height (SWH). 3.2.1. Maximum wind speed Eq. (9) is the cumulative Gumbel distribution function. V is the wind velocity (m/s), l and r are the mean and standard deviation of the wind velocity. The scale parameter, a, and the location parameter, b, are characteristic values of the Gumbel distribution function. Table 1 shows two parameters, and they can be calculated using mean values and standard deviations of the maximum instantaneous wind speed, which are extracted from the numerical weather data for a 50-year period at the two target locations.

  FðVÞ ¼ exp
exp
Y ; Y ¼ aðV
bÞ; 1 where a ¼ 0:78 r ; b ¼ l
0:45r

ð9Þ

It is assumed that the maximum instantaneous wind speed follows the Gumbel distribution. Eq. (10) expresses the relationship between the return period (T, years) and the cumulative distribution function. Eq. (11) is obtained from Eq. (9) and (10).

FðVÞ ¼ 1
VðTÞ ¼


1 T

ð10Þ

   1 T þb ln ln a T
1

ð11Þ

3.2.2. Significant wave height (SWH) Gumbel distribution function can be employed for estimating extreme waves for each return period. When accumulated wave data are not available, Eq. (12) that is the interaction formula between the fully developed SWH and wind velocity can be used [33,40]. A change in wind speed can affect SWH because the wind speed and SWH exhibit a strong correlation. 2

SWH ¼ 0:0246  ðwind velocityÞ

ð12Þ

3.2.3. Current Currents are divided into two types: wind currents and tidal currents. It is assumed that the velocity of currents, which is affected by the wind at the sea level, is approximately 1% of the wind velocity. Their velocity linearly decreases down to the seabed [7]. At Location A, the tidal current is stronger than the wind current. According to records obtained at the buoy near Location A,

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Fig. 3. Conceptual drawing of Pile Guide System.

Table 1 Scale and location parameters to compute extreme wind velocity.

Location A Location B

Scale parameter, a

Location parameter, b

0.377 0.242

21.6 26.9

Table 3 Extreme environmental loads applied to PGS (characteristic loads). Return Period (years)

the maximum velocity of the tidal current is 1.9 m/s. 0.5 m/s or less has been measured for tidal current near Location B.

3.3. Step 2: Calculation of characteristic environmental loads for a set of return periods A set of 15 return periods are selected: 30, 50, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 3000, 5000, 10,000 years. Table 2 shows the extreme environmental conditions (wind, current, and SWH) estimated on the basis of the Gumbel distribution at two target locations. These extreme environmental conditions are employed for the structural design. Table 3 shows characteristic loads acting on the PGS at the two target locations. They are estimated by the two commercial codes: ANSYS-AQWA for the floater and SESAM GeniE for the seabed truss structures. The vertical force (Z-direction force) is excluded because the PGS allows the floater to exhibit vertical motion in accordance with draft of the floater and the seawater level.

Location A X (ton)

Location B Y (ton)

X (ton)

Y (ton)

30

2:42  10

5:89  10

3:22  104

50

2:87  103

1:34  104

6:90  103

3:89  104

100

3:55  103

1:73  104

8:23  103

4:79  104

200

4:32  103

2:18  104

9:88  103

5:97  104

300

4:80  103

2:48  104

1:08  104

6:57  104

400

5:17  103

2:71  104

1:15  104

7:03  104

500

5:45  103

2:89  104

1:21  104

7:33  104

600

5:70  10

3

4

4

1:25  10

7:70  104

700

5:91  103

3:19  104

1:29  104

7:82  104

800

6:10  10

3

4

4

1:32  10

7:98  104

900

6:26  103

3:42  104

1:36  104

8:24  104

1000

6:41  10

3

4

4

1:38  10

8:29  104

3000

8:13  103

4:70  104

1:72  104

1:09  105

5000

3

4

4

1:23  105

2:11  104

1:39  105

9:01  10

10,000

3

1:03  104

1:09  10

3:05  10

4

3:32  10 3:52  10 5:33  10

6:29  104

1:90  10

3

3.4. Step 3: Structural design for each design load In the structural design step, the dimensions of the guide piles and seabed truss structures required to withstand each design load

Table 2 Extreme environmental conditions at target locations. Return Period (years)

30 50 100 200 300 400 500 600 700 800 900 1000 3000 5000 10,000

Location A

Location B

Wind (m/s)

Current (m/s)

SWH (m)

Wind (m/s)

Current (m/s)

SWH (m)

30.5 31.9 33.8 35.6 36.7 37.4 38.0 38.5 38.9 39.3 39.6 39.9 42.8 44.1 46.0

1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9

3.25 3.87 4.78 5.79 6.43 6.90 7.27 7.59 7.86 8.10 8.31 8.50 10.65 11.73 13.27

40.9 43.1 46.0 48.8 50.5 51.7 52.6 53.4 54.0 54.6 55.1 55.6 60.1 62.2 65.0

<0.5 <0.5 <0.5 <0.5 0.51 0.52 0.53 0.53 0.54 0.55 0.55 0.56 0.60 0.62 0.65

7.77 9.03 10.8 12.9 14.1 15.1 15.8 16.4 16.9 17.4 17.8 18.2 22.3 24.4 27.4

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Fig. 4. ABAQUS 3D solid model for PGS analysis.

Table 4 Dimensions of guide piles and trusses in relation to each design load. Return Period (years)

30 50 100 200 300 400 500 600 700 800 900 1000 3000 5000 10,000

Diameter at Location A

Diameter at Location B

Guide pile (m)

Truss X (m)

Truss Y (m)

Guide pile (m)

Truss X (m)

Truss Y (m)

2.86 3.10 3.43 3.78 3.99 4.14 4.26 4.36 4.44 4.51 4.57 4.63 5.23 5.52 5.92

1.53 1.66 1.84 2.03 2.14 2.22 2.28 2.34 2.38 2.42 2.45 2.48 2.80 2.96 3.17

1.92 2.08 2.30 2.53 2.67 2.77 2.85 2.92 2.97 3.02 3.06 3.10 3.50 3.70 3.97

4.40 4.80 5.20 5.75 5.95 6.10 6.25 6.35 6.45 6.55 6.65 6.70 7.45 7.90 8.30

2.51 2.73 2.96 3.27 3.39 3.47 3.56 3.62 3.67 3.73 3.79 3.82 4.24 4.50 4.73

2.95 3.22 3.48 3.85 3.99 4.09 4.19 4.25 4.32 4.39 4.46 4.49 4.99 5.29 5.56

Table 5 Classification of damage states. Damage states

Load factor

Number of failed guidepiles (EA)

Repair and replacement time (days)

Location A Non-structural damage (Insignificant) Slight structural damage (Minor) Moderate structural damage (Significant) Severe structural damage (Severe)

Location B

L (Characteristic Load) 1.5 L (Design Load)

<1

5

5

4

15

17

1.93 L

8

29

35

2.43 L

>12

46

57

are determined. Two commercial codes are employed: one is ABAQUS for the structural design; the other is PIANO for automatically changing the design variables. An ABAQUS 2D wire model is used to save iteration time when it is connected to the PIANO for cross-sectional optimization. The radii and thicknesses of the piles and truss structures are selected as the design variables. The rein-

forcement is focused upon in the Y direction because the applied load is dominant in this direction. A 3D solid model generated in ABAQUS, shown in Fig. 4, is employed to check material limit states, which include the axial tension, axial compression (column buckling and local buckling), bending, and shear stress. Finally, all of the dimensions of the piles

S.-y. Lee et al. / Structural Safety 59 (2016) 96–107

and truss structures for each design load are determined and are shown in Table 4. ASTM A135 steel is considered as the material of the structure. The capital expenditure for the PGS can be estimated based on the dimensions of the PGS for 15 design loads in the next step.

Table 6 Probability of failure for each damage state at Location A. Return period for characteristic load (years) 30

Probability of Failure (per annual)

Insignificant

Minor

Significant

Severe

3:33  10
2

4:55  10
3

1:48  10
3

4:00  10
4

50

2:00  10
2

1:67  10
3

7:14  10
4

1:82  10
4

100

1:00  10
2

7:14  10
4

3:33  10
4

1:11  10
4

200

5:00  10
3

3:13  10
4

1:25  10
4

2:17  10
5

300

3:33  10
3

1:75  10
4

6:33  10
5

9:52  10
6

400

2:50  10
3

1:32  10
4

4:52  10
5

6:21  10
6

500

2:00  10
3

8:93  10
5

2:89  10
5

3:57  10
6

600

1:67  10
3

7:63  10
5

2:41  10
5

2:86  10
6

700

1:43  10
3

6:17  10
5

1:88  10
5

2:11  10
6

800

1:25  10
3

5:13  10
5

1:52  10
5

1:61  10
6

900


3


5


5

1:27  10
6

1:11  10

4:33  10

1000

1:00  10
3

3:72  10
5

1:05  10
5

1:03  10
6

3000


4

3:33  10

6:31  10


6


6

8:26  10
8

5000

2:00  10
4

2:76  10
6

5:20  10
7

2:54  10
8

10,000


4


7


7

4:71  10
9

1:00  10

8:45  10

1:25  10 1:35  10 1:32  10

Table 7 Probability of failure for each damage state at Location B. Return period for characteristic load (years)

Probability of failure (per annual)

Insignificant
2

Minor

Significant
3

Severe


3

9:09  10
4

30

3:33  10

7:69  10

50

2:00  10
2

4:00  10
3

1:25  10
3

4:17  10
4

100

1:00  10
2

1:67  10
3

5:26  10
4

1:30  10
4

200

5:00  10
3

8:00  10
4

1:82  10
4

3:28  10
5

300

3:33  10
3

4:88  10
4

9:90  10
5

1:52  10
5

400

2:50  10
3

3:23  10
4

5:88  10
5

8:00  10
6

500

2:00  10
3

2:46  10
4

4:08  10
5

5:05  10
6

600


3

1:67  10

1:96  10


4

2:99  10
5


6

3:44  10

700

1:43  10
3

1:61  10
4

2:33  10
5

2:49  10
6

800


3

1:25  10

1:31  10


4


5

1:80  10
6

2:50  10

1:81  10

900

1:11  10
3

1:11  10
4

1:46  10
5

1:39  10
6

1000


3

1:00  10

9:48  10


5


5

1:07  10
6

3000

3:33  10
4

1:83  10
6

1:44  10
6

7:46  10
8

5000


4


6


7

1:88  10
8

1:25  10
7

3:46  10
9

10,000

2:00  10

7:84  10

1:00  10
4

2:75  10
6

1:19  10 4:82  10

103

3.5. Step 4: Relationship between the characteristic load and structural reliability for each return period For the PGS, damage states are classified into four cases (Table 5) on the basis of the number of guide piles when extreme environmental loads, which are larger than the characteristic load, are applied to the floater. The number of damaged guide-piles and the load factors for each damage state are determined by the finite element analysis. The repair and replacement time includes both the active replacement time (16 h per one guide pile) and logistic support (one day per one guide pile), which is the time for the failed components to arrive at the target site. Five days for inspection, maintenance and operation test are also required after replacement. If eight or more guide piles fail, the replacement time increases (1.5 days per one guide pile) due to re-assembly challenges. The annual probability of failure for each damage state in case of the two target locations can be calculated by using Eq. (1), and they are shown in Tables 6 and 7. The probability of failure per annum can be simply defined as the inverse of the return period of the applied load for each damage state and for each return period. Probability of failure at Location B is relatively high compared with that of Location A due to the severe environmental conditions. The relationship between the return periods of characteristic loads and annual probability of failure can vary depending on the target locations and the selected distribution function. 3.6. Step 5: LCC estimation for each structural design 3.6.1. Capital expenditure The CAPEX is the initial investment, including manufacturing costs, transport costs, and installation costs for the structure. The CAPEX can be calculated using Eq. (3), where the coefficient of manufacturing costs for the CAPEX is 1.43. It is assumed that the manufacturing cost is 70% of the CAPEX to estimate the initial investment for the whole structure [39]. The following costs per

Fig. 5. CAPEX of PGS at two target locations.

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S.-y. Lee et al. / Structural Safety 59 (2016) 96–107

Fig. 6. RISKEX of PGS at two target locations.

Fig. 7. Life-cycle cost analysis at Location A.

unit mass of steel structure are used for manufacturing costs. The guide piles are relatively simple structures, and the cost of material and fabrication is estimated at USD 2495 per unit ton. The manufacturing costs of the seabed truss structures are estimated at USD 4990 per unit ton due to their relatively complicated shape [8]. The mass of the guide piles and seabed truss structures can be estimated on the basis of the dimensions, which are determined at the structural design stage. Fig. 5 indicates the initial investments of the PGS at the two target locations. The CAPEX is pretty expensive at Location B compared with Location A because Location B has more severe environmental conditions for installing the PGS than Location A.

3.6.2. Operating expenditure It is assumed that the OPEX is 1% of the CAPEX per annum. The lifespan of the structure and the present worth factor are considered for the OPEX. The OPEX can be calculated according to Eq. (4), where the coefficient of material cost for CAPEX is 0.01.

3.6.3. Risk expenditure The RISKEX is the failure risk expenditure due to an extreme environmental load. It is the present value of replacement costs and economic loss from the expected structural damage in the future. It is estimated by Eqs. (5)–(7). The following assumptions are also employed to compute RISKEX: – The PGS structure can be used to support an LNG-BT in the near future. – The lifespan of the PGS is 50 years. – Intentionally failed components as well as guide piles, which are easy to maintain and replace, are considered. It is assumed that 4–14 guide piles fail for each damage state (C r , the cost of repair and replacement). The price of a single guide pile can vary depending on the design load. – The rental fee (C c ) of an offshore heavy lift vessel (HLV) for the replacement of the damaged guide piles: USD 300,000 per day for 1000 ton, USD 370,000 per day for 1800 ton, and USD 500,000 per day for 4500 ton [38].

S.-y. Lee et al. / Structural Safety 59 (2016) 96–107

105

Fig. 8. Life-cycle cost analysis at Location B.

– The price of LNG as fuel is approximately USD 14 per MMBTU, which corresponds to USD 327.6 per cubic meter. – The suspension of LNG sales (C e , economic loss) can be estimated from the amount of LNG sold per day (LNG sales: 53,700 m3 per day; USD 17,592,120 per day) [42]. Operational condition is the circumstance when the installation vessels can continue their work activities. 1.5 m or less of SWH are operational conditions for HLVs [36]. Accumulated wave data in two target locations are analyzed to consider probability for operation of HLVs. The chances for operation are respectively 85% and 67% at Location A and Location B. These probabilities of HLVs operation are used to calculate repair and replacement times. The replacement costs for 4–12 guide piles (Cr) and the rental fee for offshore crane vessels (Cc) are considered to compute the cost of repair and replacement. The suspension of LNG sales during the repair time is estimated for the economic loss (Ce). It is assumed that the total LNG fuel to be bunkered is 53,700 m3 per day for 13 ships per day [42]. Finally, Fig. 6 shows the RISKEX at the two target locations. Annual probability of failure is high, and relatively severe environ-

mental conditions for HLVs exist at Location B. That is why the RISKEX is also expensive at Location B compared to Location A. 3.7. Step 6: Determining the optimal reliability with the minimum LCC Finally, the set of LCCs are calculated for each structural design, and the optimal design load and reliability are determined with the minimum LCC at the two target locations. 4. Results and discussion 4.1. Determination of design load In this study, 15 extreme environmental loads are employed in designing the supporting structure for LNG-BT, and the results are compared with the original characteristic load occurring once in 100 years. Figs. 7 and 8 show the results of the LCC analysis in relation to 15 characteristic loads at the two target locations. When the strength of the PGS structure increases, the CAPEX also increases. The increasing trend of the CAPEX is very similar to that of characteristic loads. On the other hand, the RISKEX decreases when the

Fig. 9. Life-cycle cost analysis for annual probability of failure at Location A.

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S.-y. Lee et al. / Structural Safety 59 (2016) 96–107

Fig. 10. Life-cycle cost analysis for annual probability of failure at Location B.

characteristic load for the PGS increases. The RISKEX initially declines rapidly but later decreases slowly. The tendency of the CAPEX to increase is greater than that of the RISKEX to decrease at the point of a characteristic load occurring once in 500 years at Location A. The 15 return periods considered in this research are sufficient to obtain the minimized LCC. Considering a smaller interval for the return periods might be unnecessary because the difference between the 500-year LCC and the 400-year LCC is insignificant. As a result, preparation for the environmental loads occurring once in 500 years is the most economically sound strategy for the structural design of the PGS at Location A, even though the CAPEX of the structure increases. On the other hand, when the PGS is installed at Location B, the optimal return period of the characteristic load is changed from 500 years to 300 years because the CAPEX increases rapidly compared with the PGS installed at Location A. The most important value for the structural design is the optimal reliability. If an engineer employs other load factors and material factors from other regulations, the optimal environmental characteristic load can change despite the fact that the same target structure, the system, and the location are considered. However, the optimal design load and reliability cannot be altered for the same structure and target site. In other words, employing a load factor of 2.4 and a 100-year characteristic load constitutes the same design as using a load factor of 1.5 and a 500-year characteristic load. Both cases induce the same structural reliability and annual probability of failure through the LCC analysis. Although the optimal environmental characteristic load is a mutable value depending on the load factor of the design, it is quite significant in terms of acting as a bridge for studying the relationship between the structural reliability and the CAPEX. 4.2. Structural reliability Many studies addressing structure reliability for offshore structures have been carried out, and the estimated reliability has been compared with target reliability from classification societies as criteria. DNV suggests relatively high reliability for offshore structures compared with other structural standards. The PGS structure can be classified into class II (significant warning prior to the occurrence of failure in a non-redundant structure). Values of 10
4 and 10
5 per year are recommended by DNV for less serious consequences and serious consequences. The relationship

between characteristic loads and structural reliability is studied in this research, and the optimal reliabilities for three damage states of the PGS at two target locations are obtained from the relationship. Figs. 9 and 10 indicate the LCC analysis of the PGS at the two target locations, and x-axis is annual probability of failure in terms of minor consequences. Annual probability of failure for minor consequences is compared with DNV’s value for less serious consequences, and probability of failure for severe consequences is drawn a comparison with DNV’s value (10
4) for serious consequences. The optimal reliabilities of the PGS are 8:93  10
5 at Location A and 4:88  10
4 at Location B. If the PGS is installed at Location A, the optimal annual probability of failure is less than that of DNV, which means that it is economical for the PGS to be designed stronger than the structure designed in compliance with DNV’s values. On the other hand, if Location B is considered as the target location, optimal annual probability of failure with respect to three damage states increase. Location B has severe environmental conditions for the PGS compared with Location A. Initial investment can dramatically increase when the structural reliability increases at Location B. The optimal reliability from an economic point of view at Location B can conflict with safety criteria from DNV.

5. Conclusion A practical design procedure for determining the optimal design load and reliability was proposed for a newly developed offshore structure. The pile-guide system (PGS) for LNG Bunkering Terminal and two target locations near Busan city were selected for a case study. The structures were designed according to a given set of environmental loads caused by waves, currents, and winds. Gumbel distribution function was employed to estimate extreme environmental conditions, and two commercial codes were used to calculate the characteristic loads for each return period. 15 return periods (30, 50, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 3000, 5000 and 10,000 years) of characteristic loads were applied for the structural design. Life-cycle cost (LCC) analysis was performed to determine the optimal design load and reliability from an economic point of view. In order to compute the LCC, capital expenditure (CAPEX), operating expenditure (OPEX), and risk expenditure (RISKEX) were considered. The relationship between the characteristic load and structural reliability was studied on

S.-y. Lee et al. / Structural Safety 59 (2016) 96–107

the basis of the selected probabilistic model to propose a practical method for estimation of the CAPEX and the RISKEX. Finally, we obtained the optimal design load and target reliability for the offshore installation for the two target locations. At Location A (near Busan New Port), it would be economical when the PGS was designed stronger than the structure designed in compliance with the DNV’s regulations for fixed offshore structures. On the other hand, when Location B was considered as the target location, optimal annual probability of failure with respect to three damage states increased. Location B had relatively high probability of failure and severe environmental conditions for operating a heavy lift vessel (HLV) compared with Location A. Initial investment dramatically increased when the structural reliability increased at Location B. Optimal reliability from an economic point of view could conflict with DNV’s safety criteria at Location B. This case study demonstrated convincingly that optimal reliability could vary depending on the target locations with regard to the same structural system. The optimal design load and target reliability might differ depending on the type of involved structures, the economic roles of the system, and the environmental conditions at various locations. Thus, the proposed procedure for determining the optimal design load and reliability would be meaningful and applicable to design of a newly developed offshore installation at the conceptual design stage. Acknowledgements This work was supported by the Global Leading Technology Program of the Office of Strategic R&D Planning (OSP) funded by the Ministry of Knowledge Economy, Republic of Korea. References [1] Ang AH-S, De Leon D. Determination of optimal target reliabilities for design and upgrading of structures. Struct Saf 1997;19(1):91–103. [2] API. API Recommended Practice 2A-WSD (RP-2A-WSD); 2nd ed. Washington, D.C. [3] Bhattacharya Baidurya, Basu Roger, Ma Kai-tung. Developing target reliability for novel structures: the case of the Mobile Offshore Base. Marine Struct 2001;14:37–58. [4] Canadian Standards Association. General requirements, design criteria, the environment, and loads, a national standard of Canada. CAN/CSA-S471-92, 1992. [5] Laura Castro-Santos, Vicente Diaz-Casas. Life-cycle cost analysis of floating offshore wind farms. Renew Energy 2014;66:41–8. [6] Chang DJ, Chang GP. Process of offshore installation and safety design. Paju: Dongmyeong; 2013. p. 134–137. [7] Choi KS. Offshore structural engineering. Seoul: Munundang; 2013. [8] de Vries W. Final report WP 4.2 support structure concepts for deep water sites. Delft, The Netherlands: Delft University of Technology; 2007. [9] Val Dimitri V, Stewart Mark G. Life-cycle cost analysis of reinforced concrete structures in marine environments. Struct Saf 2003;25:343–62. [10] DNV. Structural reliability analysis of marine structures, classification notes no. 30.6. DNV, Norway; 1992. [11] DNV-OS-C101. Design of offshore steel structures, general (LRFD method); 2011, p. 23–24. [12] DNV-RP-C205. Environmental conditions and environmental loads; 2010. [13] Gudfinnur Sigurdsson. Guideline for Offshore Structural Reliability Analysis: Application to Jacket Platforms. Technical Report of DNV (Report No. 95– 3203); 1996. [14] Hwang H, Xu M, Huo J. Estimation of Seismic Damage and Repair Cost of the University of Memphis Buildings. Tennessee: Memphis; 1994.

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